There are angles whose measures add to 180° . Their measures are: m∠A =67°, m∠B = (2x + 20)° , and m∠C = x° . What is the measure of ∠B?
A) 31°
B) 82°
C) 62°
D) 180°
We are given that the measures of angles A, B, and C add up to 180°. Therefore, we can write the equation:
m∠A + m∠B + m∠C = 180°
Plugging in the given measures:
67° + (2x + 20)° + x° = 180°
Combining like terms:
3x + 87° = 180°
Subtracting 87° from both sides:
3x = 93°
Dividing both sides by 3:
x = 31°
Since we are looking for the measure of angle B (m∠B), we can plug in the value of x into the expression for angle B:
m∠B = 2x + 20° = 2(31°) + 20° = 82°
Therefore, the measure of ∠B is 82°. The correct answer is B) 82°.